Thompson is in a statistical dead heat with Rudy Giuliani, according to a new CNN/Opinion Research Corporation poll.

WASHINGTON (CNN) - Five days after he officially jumped into the Republican race for the White House, former Tennessee Sen. Fred Thompson finds himself in a statistical dead heat with frontrunner Rudy Giuliani, according to a new CNN/Opinion Research Corporation poll out Tuesday.

The former New York City mayor garners 28 percent nationally among registered Republicans while Thompson is only one point behind at 27 percent - well within the poll's 5 percentage point margin of error. In a similar poll taken in August, Giuliani registered 29 percent while Thompson, then not yet an official presidential candidate, was at 22 percent. (See full poll results [PDF])

CNN Senior Political Analyst Bill Schneider notes, "Thompson has the edge among evangelical Republicans and especially among his fellow southerners - that's where Thompson has made the biggest gains."

While the CNN/Opinion Research Corporation Poll shows a statistical dead heat, other recent national polls indicate Giuliani continues to hold a lead over Thompson. A CBS/New York Times poll released Monday showed Giuliani with a 5 point lead over Thompson, 27 percent to 22 percent. Meanwhile, a USAToday/Gallup poll out Monday has Giuliani with a 12 point lead, 34 percent to 22 percent.